# Lesson: Estimating and rounding

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### Lesson Objective

SWBAT estimate the results of computations with all numbers

### Lesson Plan

 Standard *6.NSO-E.18 - Estimate results of computations with whole numbers and with positive fractions, mixed numbers, decimals, and percentages. Determine reasonableness of estimates.                                                                              6.NSO-N.7 - Round whole numbers and decimals to any given place. Objective Essential Question SWBAT estimate the results of computations with all numbers When are estimations strategies useful?

Lesson Agenda

Agenda Item/ Time (Board Configuration)

5 E’s

Learning Activities

Teacher will do…

Students will do …

10 minutes

Daily Math Review (Warm-Up/ Do Now)

Use the number 27.3865. Write the value of the given digit

1. 2

2. 3

3. 8

4. 6

Use the number 146.9032. Write the value of the given digit

1. 0

2. 9

3. 2

4. 1

Students will take out homework and complete Do Now at zero noise.

5 minutes

Math Vocabulary

estimate, about, and closest to all of these mean to estimate and find an approximate answer.

10 minutes

Engage

Some real-world problems require only an estimate for an answer. Others require an exact answer. Decide whether each situation needs an estimate or an exact answer. Explain your reasoning

1. a headline noting the number of people living in China

2. the amount of money a baby sitter charges per hour

3. the width of a window screen

4. the distance from Earth to the moon

5. the hours at soccer practice in one month

6. the number of tickets to sell for a play

Students will take 5 minutes to answer these questions independently then they will turn and talk with a partner about their answers for the next 2 minutes. We will take 3 minutes to go over their responses.

15 minutes

Explore (Conceptual Development)

Each digit in a decimal has a place and a value. The value of any place is one-tenth the value of the place to its left. Fill in the place value chart below:

 0 . 4 2 6 1

Express 0.426 using words.

The last digit, 6, is in the thousandths place. So, 0.426 ends with the word thousandths.

0.426 is four hundred twenty-six thousandths

Express two and three hundredths as a decimal

And represents the decimal point. The hundredths place is the second place to the right of the decimal point.

Two and three hundredths is 2.03

We can use graph paper to compare and order decimals. The last digit is the farthest digit to the right so we always start with that digit then work our way left to see which decimal is larger.

Ex: 0.89 and 0.889

Step 1: fill in one number per square on your graph paper and line up decimals so that it looks like this.

 0 . 8 9 0 0 . 8 8 9

Step 2: fill in 0 for any open square

Step 3: begin with the farthest left to see which is larger. (we do this because the numbers on the left are 1/10 larger than each number to the right of it.

Since 0 = 0 we move to the next Column. 8 = 8 so we move to the next column 9 is larger than 8 so we know that 0.89 is larger than 0.889

Students actively take notes in guided notes and engage in discussion when asked to do so.

15 minutes

Explain

(Guided Practice)

Now that we know how to compare and order decimals let’s take a look at rounding decimals.

Steps to round decimals:

Step 1: underline the place it is asking you to round to

Step 2: circle the number to the right of that place

Step 3: if the circled number is 5 or larger the underlined number goes up. If it is less than 5 the underlined number stays the same.

Try these with the class

Round 4.2683 to the nearest tenth.

Round 4.2683 to the nearest one.

So let’s recap… we have learned how to compare and order decimals and how to round decimals. Now that we know how to do these things we have to ask ourselves why these things are useful? Where are they used in the real world?

Well the answer is they are used when we estimate sums and differences. You can estimate a result before you calculate. Then, if your answer is close to your estimate, you know that is probably is correct. It is also useful when estimating the cost of a grocery bill or population. Can anybody think of any other use’s for rounding to estimate?

You already know how to round so now you just apply that knowledge to estimating.

Ex: Carrots cost \$2.71, peppers cost \$1.73 and broccoli cost \$1.10. estimate the total cost of the vegetables but rounding to the nearest whole dollar.

(have them underline each dollar and circle each tenths place {the number to the left} to get

\$2.71  ~ 3.00

\$ 1.73 ~ \$2.00

\$1.10 ~ \$1.00

So the estimated cost of the vegetables is \$6.00

Try this again but this time round to the nearest ten cent. (do this again but have them underline the tenths place and circle the hundredths place.

Which estimate do you think is closer?

Which estimate do you prefer and why?

20 minutes

Extend (Independent Practice)

Students will do a worksheet with 15-20 rounding and estimation questions on it. They will spend 15 minutes on the handout then 5 minutes to trade and grade.

5 minutes

Evaluate

(Assessment/ Closure)

When you estimate 320.18 + 46 + 8.68 by rounding to tens, what value do you get?

a. 370     b. 374.9      c. 374       d. 380

### Lesson Resources

 6 NSO E 18GN   Classwork 536